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Quasianalytic Ilyashenko Algebras
Patrick Speissegger
Journal:

Canadian Journal of Mathematics / Volume 70 / Issue 1 / 01 February 2018

Published online by Cambridge University Press:

20 November 2018, pp. 218-240

Print publication:

01 February 2018
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We construct a quasianalytic field $\mathcal{F}$ of germs at $+\infty $ of real functions with logarithmic generalized power series as asymptotic expansions, such that $\mathcal{F}$ is closed under differentiation and log-composition; in particular, $\mathcal{F}$ is a Hardy field. Moreover, the field $\mathcal{F}\,\circ \,\left( -\text{log} \right)$ of germs at ${{0}^{+}}$ contains all transition maps of hyperbolic saddles of planar real analytic vector fields.